A "change of basis" is an action performed in linear algebra, whereby a change in fundamental structure yields an entirely new viewpoint. This blog began as a record of a pedagogical change of basis for me, and continues as an ongoing account of my thoughts as I design and direct courses in mathematics at the University of North Carolina, Asheville.

Monday, August 28, 2006

I'm just about to wrap up another day, and I thought I'd check in on the ol' blog, not having written anything for a couple of days.

Things have been going pretty well in MATH 365, as far as I can tell. I spent a couple more hours on Sunday morning putting together some Mathematica programs to help people deal with various issues (visualizing vector addition and getting practice with matrix multiplication), and then writing a brief somethingorother for Wednesday's class on mathematical writing: I should be all set for that class's "Write a Bad Paper" exercise. I'm looking forward to it!

I was pleased to get a chance this morning to work one-on-one with Irene, one of the students I'd not met before this class. She's putting a lot of effort into the class, and I admire her courage, because I know she was a little hesitant about her preparedness for the course. I look forward to learning more about the other students in the class with whom I've not yet become acquainted.

I experienced a minor setback in getting the course to qualify as a Writing Intensive course this afternoon, when I was informed by our school's diligent WI committee chair that I'd inadvertently filled out the wrong form in constructing the WI application. No worries: some relatively minor modifications and my current document will serve, with a few frills added for trim. I hope to finish that up tomorrow, depending on the busyness of my schedule.

Class today (Monday) went well, as far as I could tell. I had a better feeling about it than I did about last Friday's class: Friday seemed to go by so quickly, and I got the sense that on that day we didn't get to the heart of the topics we discussed. Today, on the other hand, there was just a single focal topic (the use of matrix multiplication and matrix powers in understanding a simple stochastic economic model), so our attention was more singularly drawn. Although I had originally planned on using the PDF outline I'd posted on the course website as a guide through the trenches, I decided after all to just throw them into the pool and see if they sank or swim.

And they swam, every last one of 'em. Not a single team failed to come up with and elaborate upon the idea of matrix multiplication. I wish I'd had more chance to work with each team individually, but from the floating and flitting about the room I was able to accomplish, I noted a good deal of creative work on the part of many students, and for the most part there was robust communication within each team. (After class, a few folks noted a kink or two here and there, owing to relative reticence of certain team members, or to unfamiliarity with one another, but these issues should not be hard to resolve. On no one's part was there any malice or animosity.)

I spent about half an hour earlier this evening in sending e-mails to a few of the folks in the class, polling them to see how they felt their respective teams managed today. Every response I've received so far has been positive, so I'm heartened. I've been informed by one of its members that even the one team I was a little concerned about fared quite well today. Rejoice!